An Empirical Bayes Approach to Estimating Dynamic Models of Co-regulated Gene Expression

Time-course gene expression datasets provide insight into the dynamics of complex biological processes, such as immune response and organ development. It is of interest to identify genes with similar temporal expression patterns because such genes are often biologically related. However, this task is challenging due to the high dimensionality of such datasets and the nonlinearity of gene expression time dynamics. We propose an empirical Bayes approach to estimating ordinary differential equation (ODE) models of gene expression, from which we derive similarity metrics that can be used to identify groups of genes with co-moving or time-delayed expression patterns. These metrics, which we call the Bayesian lead-lag R2 values, can be used to construct clusters or networks of functionally-related genes. A key feature of this method is that it leverages biological databases that document known interactions between genes. This information is automatically used to define informative prior distributions on the ODE model's parameters. We then derive data-driven shrinkage parameters from Stein's unbiased risk estimate that optimally balance the ODE model's fit to both the data and external biological information. Using real gene expression data, we demonstrate that our biologically-informed similarity metrics allow us to recover sparse, interpretable gene networks. These networks reveal new insights about the dynamics of biological systems.